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Actually Isogeometric Analysis (IGA) have proven high accuracy and efficacy in dynamical problems, openning possibilities to improve the traditional FEM models. The aim of this paper is to test the response of IGA for free vibration problems of plane stress and structures. Based on numerical applications, IGA models have their convergence and accuracy checked and compared with those developed in FEM and GFEM. The results shows high accuracy for IGA models, and reinforce its way as a promising tool.Keywords: Isometric Analysis, Free Vibration, Plane Stress

Neste trabalho o refinamento k da An´alise Isogeom´etrica (AIG) ´e aplicado ao problema de concentrac¸ ˜ao de tens˜oes. As func¸ ˜oes bases NURBS s˜ao obtidas a partir da definiç˜ao da geometria e aplicadas na aproximac¸ ˜ao do campo desejado (conceito isoparam´etrico). Aplicase o refinamento, elevando-se a ordem das funç˜oes bases e inserindo-se um novo n´o, dentro do vetor de n´os, logo na sequˆencia. Com isso elevam-se as funções de ordem p para q, e a continuidade de Cp􀀀1 para Cq􀀀1, sendo esta uma grande vantagem no uso do refinamento k. O refinamento k da AIG ´e analisado e tamb´em comparado ao refinamento hp, ressalta-se tamb´em a utilizaç˜ao da AIG em problemas que envolvem concentraç˜ao de tens˜oes e a eficiˆencia do refinamento k.

In the context of dynamic analysis of structures, one of the limitations of the Finite Element Method (FEM) is the difficulty of approaching the high frequencies. This lack of precision becomes more significant as the loading excite modes with higher frequencies. Aiming at address this problem one may use the Finite Element Method Generalized / Extended (GFEM /XFEM) to enrich the approximation space and better represent these high frequency modes.Despite the excellent properties of GFEM / XFEM as high accuracy, application versatility and excellent convergence rates, there are aspects that still limit its applicability as the numerical instability associated with this enrichment process even in well-placed boundary value problems. GFEM/XFEM matrices may be ill-conditioned, which may result in a accuracy loss, and even resulting in numerically singular matrices. In this work two proposals are presented to circumvent the GFEM sensitivity problem. Examples of one-dimensional transient analysis are presented and results are discussed analyzing the effects of adopting the preconditioning of enrichment functions strategy.Keywords: Dynamic Analysis, GFEM, Partition of Unity, Conditioning, SGFEM.

The Generalized Finite Element Method Applied to Free Vibration of Framed Structures

Submitted by Rosangela Silva (rosangela.silva3@unioeste.br) on 2023-02-03T21:56:06Z No. of bitstreams: 2 Marcos Alexandre Arndt.pdf: 433315 bytes, checksum: 2f3625259df5d7f728bfe28769f847f2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Made available in DSpace on 2023-02-03T21:56:06Z (GMT). No. of bitstreams: 2 Marcos Alexandre Arndt.pdf: 433315 bytes, checksum: 2f3625259df5d7f728bfe28769f847f2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2009-07-22 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES The Brazilian municipality presented significant urbanization process, what caused the expansion of urban areas, and consequently increased the impermeable areas. The measure that the city is urbanized increases the peak discharge resultants of the water runoff, what can provoke problems as floods of closeness areas to the drainage channels. Know the influence of the water runoff in watershed is primordial for its management, and estimations or the sceneries of future occupations helps to support the address planning adapted for the Brazilian watershed. Starting from this problematic situation this work looked for to esteem the peak discharge of the Cascavel River, in function of the changes in the soil use in the watershed, and the precipitations with different intensities and return period, creating hypothetical sceneries of urban expansion starting from the Soil Conservation Service hydrologic model. Was verified that as the impermeable areas rise it promotes considerable increase of the peak discharge, and that this increase is more significant during precipitations with smaller period return, creating Hypothetical scenarios of urban expansion from the hydrologic model Soil Conservation Service. It was found that the increase in impermeable areas at a rate of 50% and 80% led to the increase of 3.2% and 5.1% of the value of CN, and 29.5% of the volume of peak discharges, and that this increase is more significant rainfall during the period of lower return, could cause a increase of the occurrence of floods in the drainage channels of watershed. Therefore aiming the need of the consolidation of a plan director of urban drainage for the studied area. Os municípios brasileiros apresentaram, ao longo das últimas décadas, significativo processo de urbanização, o que ocasionou a expansão de áreas urbanas, e consequentemente aumento das áreas impermeáveis. À medida que a cidade se urbaniza, ocorre aumento das vazões máximas resultantes do escoamento superficial, o que pode provocar problemas como inundações de áreas ribeirinhas aos canais de drenagem. Conhecer a influência do escoamento superficial em bacias hidrográficas é primordial para o seu gerenciamento e as estimativas de futuros cenários de ocupação servem de suporte para direcionar um planejamento adequado para as bacias hidrográficas brasileiras. Considerando estas questões, este trabalho buscou estimar as vazões máximas do rio Cascavel, em função das mudanças no uso do solo na área da bacia hidrográfica e de precipitações com diferentes intensidades e período de retorno, criando cenários hipotéticos de expansão urbana, a partir do modelo hidrológico Soil Conservation Service. Foi constatado que o aumento das áreas impermeáveis, na proporção de 50 e 80%, acarretou um aumento de 3,2 e 5,1% do valor de CN e até 29,5% do volume das vazões máximas e que este aumento é mais expressivo durante precipitações com período de retorno menor, podendo ocasionar aumento da ocorrência de enchentes nos canais de drenagem de bacias hidrográficas. Portanto, apontando a necessidade da consolidação de um plano diretor de drenagem urbana para a área de estudo.